提出一种可适应新情境的反事实回归方法,提升决策可靠性。
Semiparametric Counterfactual Regression
- 基于半参数理论与随机优化,构建双重稳健估计器
- 在广泛风险函数下实现√n一致性与渐近正态性
- 适合需快速响应政策变化的决策场景
我们研究反事实回归,旨在将输入特征映射到与观测数据中不同的假设情景下的结果。该方法在需要快速适应治疗模式突变的决策中尤为有用。本文提出一种双重稳健型估计器,在通用框架下支持广泛的损失函数和灵活约束,结合半参数理论与随机优化工具。通过增量干预增强适应性,同时保持与标准方法的一致性。我们将目标因果效应定义为随机优化问题的最优解,并设计高效估计策略,可利用现代优化算法的快速发展。我们分析了收敛速率并刻画了渐近分布,结果表明所提估计器对一大类问题可实现√n-一致性与渐近正态性。数值实验验证了其在未见反事实场景下的有效性,且保持参数级收敛速度。
原文摘要 · Abstract (English)
We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in treatment patterns is essential. We propose a doubly robust-style estimator for counterfactual regression within a generalizable framework that accommodates a broad class of risk functions and flexible constraints, drawing on tools from semiparametric theory and stochastic optimization. Our approach uses incremental interventions to enhance adaptability while maintaining consistency with standard methods. We formulate the target estimand as the optimal solution to a stochastic optimization problem and develop an efficient estimation strategy, where we can leverage rapid development of modern optimization algorithms. We go on to analyze the rates of convergence and characterize the asymptotic distributions. Our analysis shows that the proposed estimators can achieve $\sqrt{n}$-consistency and asymptotic normality for a broad class of problems. Numerical illustrations highlight their effectiveness in adapting to unseen counterfactual scenarios while maintaining parametric convergence rates.
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